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Ok, since I seem unable to explain my idea any other way, here is a very rough draft. My first question is if anyone thinks this is actually doable.

If you think it is doable, you are welcome to help me with my wording, grammar and general style of writing.

Content wise I am especially unsure about the SCP's current location, as in 'is a ancient temple to cliché'? Also if talking about how it affects reality when moved actually contradicts its own nature.

Hmmm, I thought this over, and decided to add one thing: The sceptre only affects itself, all records about it and what ever it touches directly. So it rewrites history on some scale, but does not recreate reality if ever moved.
Why am I adding this? If it would affect everything about itself, you wouldn't be able to do much more that open the door and maybe set one foot inside its chamber. At that point, its location would be changed from 'upon a altar of stone in a closed room' to 'upon a altar of stone in an opened room with one person inside it'. Then it would rewrite reality so that it would have always been like this, and will always be like this, so whoever tried to walk inside would be unable to move ever again.
Additionally, when talking about its effects when being moved, one would be unable to speak in certain terms, e.g. 'after it was moved, everyone remembered it always being there'.
But saying 'if it would be moved, we would remember it being always at the new location.
And now I am just writing out my thoughts, therefore I am ending this here.

I actually just wanted an initial response, like: 'has some potential, try it for real' or 'hopeless, better kill it now'. when even one person says I should try this for real then I will create a proper sandbox.

At that point, its location would be changed from 'upon a altar of stone in a closed room' to 'upon a altar of stone in an opened room with one person inside it'. Then it would rewrite reality so that it would have always been like this, and will always be like this, so whoever tried to walk inside would be unable to move ever again.

That's interesting.

How would the foundation actually discover its anomalous effect then if it rewrites everything?

This is exactly the reason why I made it so that it does not do that. Therefore this:

Hmmm, I thought this over, and decided to add one thing: The sceptre only affects itself, all records about it and what ever it touches directly. So it rewrites history on some scale, but does not recreate reality if ever moved.

You can tell me that I should sandbox this. Done that.
You can tell me that my draft is too rough.
You can tell me to forget this idea now, so I don't make everything worse.
I have nothing against it and kind of expect it at this point.

I'm going to have to agree with soullesshuman, this part is by far the best idea you've got here:

If it would affect everything about itself, you wouldn't be able to do much more that open the door and maybe set one foot inside its chamber. At that point, its location would be changed from 'upon a altar of stone in a closed room' to 'upon a altar of stone in an opened room with one person inside it'. Then it would rewrite reality so that it would have always been like this, and will always be like this, so whoever tried to walk inside would be unable to move ever again.

If that's a problem, you should just figure out a way to write around it.